Abstract
The BFGS method is one of the most effective quasi-Newton algorithms for minimization-optimization problems. In this paper, an improved BFGS method with a modified weak Wolfe–Powell line search technique is used to solve convex minimization problems and its convergence analysis is established. Seventy-four academic test problems and the Muskingum model are implemented in the numerical experiment. The numerical results show that our algorithm is comparable to the usual BFGS algorithm in terms of the number of iterations and the time consumed, which indicates our algorithm is effective and reliable.
Highlights
With the development of the economy and society, a large number of optimization problems have been emerged in the fields of economic management, aerospace, transportation, national defense and so on
Where xk is the current iteration point, xk+1 is the iteration point, αk is the step length, and dk is the search direction that is obtained by solving the quasi-Newton equation: (3)
From the results shown in the figures, the NI, NFG, and CPU time of the algorithm constructed in this paper are generally better than those of the standard BFGS algorithm
Summary
With the development of the economy and society, a large number of optimization problems have been emerged in the fields of economic management, aerospace, transportation, national defense and so on. The BFGS method may fail under inexact line search techniques. The global convergence of the improved BFGS method (MBFGS) is discussed by Li et al [14]. Yuan et al [15] improved the WWP line search technique and studied the new line search technique that has global convergence in the BFGS and PRP methods. Their improved line search technique (MWWP) is formulated as follows:.
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